一维谐振子的Hamilton算符为-|||-=dfrac (1)(2m)(p)^2+dfrac (1)(2)m(omega )^2(x)^2 (1)-|||-x与p满足基本对易式-|||-[ x,p] =xp-px=ih (2)-|||-引入无量纲算符-|||-=sqrt (dfrac {momega )(k)}x , =dfrac (1)(sqrt {mah)}P-|||-=dfrac (1)(sqrt {2)}(a+ip) , ^+=dfrac (1)(sqrt {2)}(Q-iP)-|||-(a)计算[Q,P], [ a,(a)^+] [ a,(a)^+a] ,[ (a)^+,(a)^+a] ;-|||-(b)将H用a、 ^+ 表示,并求出全部能级;-|||-(c)在能量表象中,计算a、 ^+ Q、P、x、p的矩阵元.